(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

From the average separation between air molecules at STP, and their mean speed, estimate how long it would take one molecule to move into the region occupied by another. Assume that air consists mainly of nitrogen molecules.

2. Relevant equations

1/2mv^2 = 3/2KT

3. The attempt at a solution

Distance between molecules at STP:

(6.02 x 10^23) x D^3 = 22.4 x 10^-3 m^3

D^3 = 3sqrt 22.4x10^-3 / 6.02 x 10^23

D = 3.34 x 10^-9 m

Since mass of N2 = 28 g/ mol, I used this to find the average velocity of the molecules:

1/2mv^2 = 3/2KT

v(rms) = sqrt(3KT/m)

= sqrt (3K (273) / .028 kg

= 6.35 x 10^-10 m/s

I then just plugged my two answers from above into the velocity equation,

velocity = distance/time

time = D/V

time = 3.34 x 10^-9 / 6.25 x 10^-10 =5.3 seconds

Does what I did make sense? The velocity looks awfully small, so I'm not sure. Any help appreciated!

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# Homework Help: Kinetic Theory

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